An equation of the line that passes through the pair of points (0,4) and (6, −3) in slope-intercept form is y = -7x/6 + 4.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (-3 - 4)/(6 - 0)
Slope (m) = -7/6
At data point (0, 4) and a slope of -7/6, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 4 = -7/6(x - 0)
y = -7x/6 + 4
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A random sample of 500 people were classified by their ages into 3 age-groups: 29 years and younger, 30 to 64 years, and 65 years and older. Each person from the sample was surveyed about which of 4 major brands of cell phone they used. Their responses were compiled and displayed in a 3-by-4 contingency table. A researcher will use the data to investigate whether there is an association between cell phone brand and age-group
To investigate whether there is an association between cell phone brand and age-group, the researcher can conduct a chi-squared test of independence.
This test compares the observed frequencies in the contingency table to the expected frequencies if there were no association between the variables. If the test results in a p-value less than the chosen significance level (usually 0.05), then the researcher can reject the null hypothesis of no association and conclude that there is evidence of an association between cell phone brand and age-group. The degrees of freedom for this test would be (3-1) * (4-1) = 6.
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Answer:1000
Step-by-step explanation:what about 1000 people
Grace has 16 more shoes. Than mark gave grace 12 shoes. Mark then realized he has half as many shoes as grace. How many shoes does grace end up with?
Mark originally had 28 shoes.
Now we can use the equation for Grace's number of shoes to find her final count:
Grace = x + 16 = 28 + 16 = 44
So Grace ends up with 44 shoes.
Grace has 16 more shoes Mark. After Mark gave her 12 shoes, he realized has half as many shoes as Grace. What is the final number of shoes that Grace has?
Let's start by setting up an equation to represent the given information:
Let the number of shoes Mark has be represented by "x"
Grace has 16 more shoes than Mark:
Grace = x + 16
Mark gives Grace 12 shoes, so Grace now has:
Grace = x + 16 + 12 = x + 28
Mark realized he has half as many shoes as Grace:
x = 0.5(x + 28)
Simplifying this equation:
x = 0.5x + 14
0.5x = 14
x = 28
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Movie Galore Video Store is open every day of the year. To rent movies from the store, a person has to pay an annual membership fee of $20, plus $2. 50 for each movie rented. To reduce the chance that movies are returned late, members are not allowed to rent more than 10 movies per day. Billy decides to become a member of the video store. Let x represent the number of movies that Billy could rent next year, and let f (x) represent the amount (in dollars) that he would pay the store as a result. Then f (x) is a function of x. What is the domain D and range R of f (x)?
The domain of the function f(x) is {x | 0 ≤ x ≤ 3650} and the range is {f(x) | 20 ≤ f(x) ≤ 9145}, where f(x) represents the amount Billy would spend to rent x films.
The domain D of the function f(x) is the collection of all possible values for x. In this scenario, because Billy is not permitted to rent more than ten films every day, the maximum number of films he may rent in a year is ten times the number of days in a year, or 10 x 365 = 3650 films.
Furthermore, because he must pay a membership fee of $20 regardless of how many movies he rents, the minimum number of movies he could rent in a year is zero. As a result, the domain of the function f(x) is as follows:
D = {x | 0 ≤ x ≤ 3650}
The range R of the function f(x) is the collection of all possible values for f(x). In this scenario, the function: returns the amount Billy would spend to rent x films.
f(x) = 2.5x + 20
where 2.5x is the rental charge for x films and 20 is the membership fee. Because x can be any value between 0 and 3650, the smallest value that f(x) can be is:
f(0) = 2.5(0) + 20 = 20
and f(x) has the following maximum value:
f(3650) = 2.5(3650) + 20 = 9145
As a result, the function f(x) has the following range:
R = {f(x) | 20 ≤ f(x) ≤ 9145}
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What can be the universal sets from which the following substes can be formed? a) set of cricket players of class 9.
b)set of cricket players of the school.
c)The set of odd numbers less than 10.
The only option that represents the universal set from the subsets is:
B: A set of cricket players of the school.
How to identify the universal set?The universal set is defined as a set that is said to consist of all the elements or objects, which includes its own elements. This universal set is represented by just a symbol 'U'
Now, a subset is also defined as a part of the universal set which is basically a group under the universal set.
Now, from the given options, the only one that could possible represent a universal set of all the options given is "a set of cricket players of the school."
Therefore we conclude that Option B provides the correct answer to the universal set definition.
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A path 3 feet wide surrounds a rectangular garden that has a length of 20 feet and a width of 12 feet. Find
the area of the path.
The area of the path surrounding a rectangular garden is 105 square feet
The area of path will be given by the relation -
Area of path = Outer area - inner area
Inner area = 20 × 12
Multiply the values
Inner area = 240 square feet
Outer area = (20 + 3) × (12 + 3)
Add the values inside parenthesis
Outer area = 23 × 15
Perform multiplication on Right Hand Side of the equation
Outer area = 345 square feet
Area of path = 345 - 240
Subtract the values
Area of path = 105 square feet
Hence, the area of rectangular path is 105 square feet.
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Qn in attachment . ..
Answer:
Step-by-the answer is (a) 16
Which of the following is a counterexample for the following statement?
“If a line intersects a circle, then it intersects it in two points.”
According to the information, and example of a counterexample is: A line can cross the circle only at one point.
What would be a counterexample for this statement?To find a counterexample to this statement we must read it carefully and identify the main idea of it. In this case you are stating that a line always crosses a circle at two points.
Later we must analyze this statement and evaluate if it is true or false. In this case it is false because we can make a line that crosses a circle only once. So, the counter example sentence would be.
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In ΔWXY, x = 4.7 cm, y = 7.9 cm and ∠W=162°. Find the area of ΔWXY, to the nearest 10th of a square centimeter.
The area of the triangle to the nearest tenth is 5.8cm²
What is area of a triangle?A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices. A triangle is also a polygon. Examples of triangle include, isosceles, equilateral , scalene e.t.c
The area of a triangle is expressed as;
A = 1/2 b h for right angle triangle and A = absinC for others.
Here; x = 4.7, y = 7.9, W = 162
area = 1/2× 4.7 × 7.9 sin162
= 1/2 × 4.7 × 7.9 × 0.31
= 5.8 cm²( nearest tenth)
Therefore the area of the triangle is 5.8cm²
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In triangle STU as equals 50 inches to equals 58 inches and you equals 27 inches find the measure of angle us to the nearest 10th of a degree
The measure of the angle ∠S, obtained using the law of cosines is about 59.4°
What is the law of cosines?The law of cosines states that the square of the length of a side of a triangle is equivalent to the sum of the squares of the other two sides less the product of the length of the other two sides and the angle between them. Mathematically; a² = b² + c² - 2·b·c·cos(A)
Where;
a, b, and c = The length of the sides of the triangle
A = The angle between b and c
The lengths of the sides of the triangle, obtained from a similar triangle are;
s = 50 inches, t = 58 inches, and u = 27 inches
The measure of the angle ∠S is required
The angle ∠S is the angle facing TU or the side s
According to law of cosines, we get;
s² = t² + u² - 2·t·u·cos(∠S)
Therefore;
50² = 58² + 27² - 2 × 58 × 27 × cos(∠S)
2 × 58 × 27 × cos(∠S) = 58² + 27² - 50²
cos(∠S) = (58² + 27² - 50²)/(2 × 58 × 27)
∠S = cos((58² + 27² - 50²)/(2 × 58 × 27)) ≈ 59.4°
The measure of the angle ∠S is about 59.4°
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questions.
1) Choose the correct name for the set of numbers.
{..., -3, -2, 1, 0, 1, 2, 3, ...}
erc
The set of numbers is an example of the integers.
What is the best name for the set of numbers?The set of numbers is an example of the integers. Integers are whole numbers (positive or negative) and zero. They are often represented by the symbol "Z". In this set, we have all the whole numbers from negative infinity to positive infinity, including negative and positive 3, 2, 1, 0, and all the numbers in between. The use of ellipses indicates that the set goes on indefinitely in both directions. It is worth noting that 1 appears twice in the set, indicating that sets of integers may have repeated elements. Overall, the set of numbers shown is an infinite set of integers.
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The original selling price of a jacket was s dollars. The selling price was then changed on two occasions by the store owner. Its price is now represented by 0. 85 (1. 4s). Which expression could explain what happened to the price of the jacket?
The expression 0.85(1.4s) explains what happened to the price of the jacket through the two changes made by the store owner.
The original selling price of the jacket was s dollars.The store owner made the first change, increasing the selling price by 40%. This can be represented by multiplying the original price (s) by 1.4: 1.4s.The store owner then made a second change, reducing the selling price by 15%. This can be represented by multiplying the new price (1.4s) by 0.85: 0.85(1.4s).So, the expression 0.85(1.4s) explains what happened to the price of the jacket through the two changes made by the store owner.
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Joe bought g gallons of gasoline for $2.85 per gallon and c cans of oil for $3.15 per can. What expression can be used to determine the total amount Joe spent on gasoline and oil?
The expression to represent the situation is 2.85g + 3.15c.
How to represent sentence with an expression?Joe bought g gallons of gasoline for $2.85 per gallon and c cans of oil for $3.15 per can.
An algebraic expression is made up of variables and constants, along with algebraic operations such as addition, subtraction, division, multiplication etc.
Therefore, the expression that can be used to determine the total amount Joe spent on gasoline and oil can be calculated as follows:
Therefore,
total cost = 2.85g + 3.15c
where
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Which pair of lines in this figure are perpendicular?
A.
lines B and F
B.
lines F and D
C.
lines C and E
D.
lines A and D
Answer:
D. Lines A and D are perpendicular.
DAnswer:
Step-by-step explanation:
A jewelry company purchases a necklace for $24. If they mark it up 36% to sell it at their store, what is the selling price of the necklace?
The selling price of the necklace at the store is $32.64.
To calculate the selling price of the necklace, we will first find the markup amount and then add it to the original cost.
Markup = (Original Cost) x (Markup Percentage)
Markup = $24 x 36% = $24 x 0.36 = $8.64
Now, add the markup amount to the original cost to find the selling price:
Selling Price = Original Cost + Markup
Selling Price = $24 + $8.64 = $32.64
So, the selling price of the necklace at the store is $32.64.
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Which is a function of a protein macromolecule? a. keeping organisms warm b. providing quick energy for cells c. moving material in and out of cells d. passing traits to offspring
One if the functions of a protein macromolecule is: c. moving material in and out of cells
What is the Function of a Protein Macromolecule?Proteins can be described as a complex macromolecules that are responsible for several key functions such as the regulation of cells, tissue, and organs of living organisms including their structure.
Proteins also help in performing the following:
Regulation of gene expression
Structural support, and
Many other cellular processes.
Therefore, a function of a protein macromolecule is: c. moving material in and out of cells.
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A pet boarder keeps a dog-to-cat ratio of 5:2. If the boarder has room for 98 animals then how many of them can be dogs
The pet boarder can accommodate 70 dogs.
To determine the number of dogsLet's calculate how many dogs and cats the pet boarding facility can hold using the ratio of dogs to cats, which is 5:2.
First, we can figure out how many parts there are in the ratio: 5 + 2 = 7.
This indicates that there are 7 equal components in the ratio, 5 of which are dogs and 2 of which are cats.
We need to multiply the result by the number of dog components (5) after dividing the total number of parts (7) into the 98 available locations to get the number of dogs:
Number of dogs = (5 / 7) * 98
Number of dogs = 70
Therefore, the pet boarder can accommodate 70 dogs.
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PLEASE ANSWER ASAPPP!!!!!
Using the following equation, find the center and radius:
x2 − 4x + y2 + 8y = −4
The center is located at (−2, −4), and the radius is 4.
The center is located at (2, −4), and the radius is 4.
The center is located at (−2, −4), and the radius is 16.
The center is located at (2, −4), and the radius is 16
The center is located at (2, −4), and the radius is 4.
To find the center and radius of this equation, we need to complete the square for both the x and y terms.
Starting with the x terms:
x^2 - 4x
To complete the square, we need to add and subtract (4/2)^2 = 4:
x^2 - 4x + 4 - 4
Now we can simplify:
(x - 2)^2 - 4
And for the y terms:
y^2 + 8y
We need to add and subtract (8/2)^2 = 16:
y^2 + 8y + 16 - 16
Simplifying:
(y + 4)^2 - 16
Now we can rewrite the original equation:
(x - 2)^2 - 4 + (y + 4)^2 - 16 = -4
Combining like terms:
(x - 2)^2 + (y + 4)^2 = 4
This is in the form of a circle:
(x - h)^2 + (y - k)^2 = r^2
Where the center is (h, k) and the radius is r.
So the center is located at (2, -4) and the radius is 4.
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The hypotenuse of a right triangle measures 29 cm. One leg is 1 cm shorter than the other. What are the lengths of the legs?
The length of the legs are 20 cm and 21 cm
What is the length of the legs?The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
We know that from the Pythagoras theorem;
[tex]c^2 = a^2 + b^2[/tex]
Let the hypotenuse be c and the other two sides be a and b
We have that;
[tex]29^2 = x^2 + (x -1)^2\\841 = x^2 + x^2 - 2x + 1\\841 = 2x^2 - 2x + 1\\2x^2 - 2x + 1 - 841 = 0\\2x^2 - 2x - 840 = 0\\x = -20 or 21[/tex]
Since length can not be negative, x = 21 cm
Thus the other leg is 20 cm
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Abde is a rectangle on coordinate axis, the sides of the rectangle are parallel to the axes what are the coordinates of b and d
The coordinates of point D would be (0,y) where y is the vertical distance between points A and D.
How to find the exact location of point A and the dimensions of the rectangle?Without knowing the exact location of point A and the dimensions of the rectangle, it is impossible to determine the coordinates of points B and D with certainty.
However, if we assume that point A is located at (0,0), and the length and width of the rectangle are given by the horizontal and vertical distances between points A and B, and between points A and D, respectively, we can find the coordinates of points B and D.
For example, if the length of the rectangle is 5 and the width is 3, then point B would be located at (5,0) and point D would be located at (0,3).
In general, the coordinates of point B would be (x,0) where x is the horizontal distance between points A and B, and the coordinates of point D would be (0,y) where y is the vertical distance between points A and D.
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The height, h, in feet of a ball suspended from a spring as a function of time, t, in seconds can be modeled by the equation h = negative 2 sine (pi (t one-half)) 5. which of the following equations can also model this situation? h = negative 2 cosine (pi t) 5 h = negative 2 cosine (pi (t one-half)) 5 h = 2 cosine (pi t) 5 h = 2 cosine (pi (t one-half)) 5
The correct answer for the equation is [tex]h = -2cos(\pi t) + 5[/tex] . The correct option is (1)
Given:
[tex]h= -2sin(\pi\tfrac{t}{2} )[/tex]
Examine the answer choices:
[tex]h = -2cos(\pi t) + 5[/tex]
Amplitude: |-2| = 2 (same as the given equation)
Frequency: π (same as the given equation)
Phase Shift: None (different from the given equation)
[tex]h = -2cos(\pi (t/2)) + 5[/tex]
Amplitude: |-2| = 2 (same as the given equation)
Frequency: π/2 (different from the given equation)
Phase Shift: None (different from the given equation)
[tex]h = 2cos(\pi t) + 5[/tex]
Amplitude: |2| = 2 (different from the given equation)
Frequency: π (same as the given equation)
Phase Shift: None (different from the given equation)
[tex]h = 2cos(\pi(t/2)) + 5[/tex]
Amplitude: |2| = 2 (different from the given equation)
Frequency: π/2 (different from the given equation)
Phase Shift: None (different from the given equation)
The correct equation is [tex]h = -2cos(\pi t) + 5[/tex] .The correct option is (1).
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Antonia read an article that said 26% of Americans can speak more than one language. She was curious if
this figure was higher in her city, so she tested H, :p=0. 26 vs. H, :p > 0. 26, where p represents the
proportion of people in her city that can speak more than one language.
Antonia took a sample of 120 people in her city found that 35% of those sampled could speak more than
one language. The test statistic for these results was z ~ 2. 25, and the corresponding P-value was
approximately 0. 1. Assume that the conditions for inference were met.
Is there sufficient evidence at the a= 0. 05 level to conclude that the proportion of people in her city
that can speak more than one language is greater than 26%?
There is not sufficient evidence at the α=0.05 level to conclude that the proportion of people in Antonia's city that can speak more than one language is greater than 26%.
Here's a step-by-step explanation:
1. Identify the null hypothesis (H₀) and the alternative hypothesis (Hₐ): H₀: p = 0.26, Hₐ: p > 0.26.
2. Determine the significance level (α): α = 0.05.
3. Calculate the test statistic (z): In this case, z ≈ 2.25.
4. Determine the P-value: The P-value is given as approximately 0.1.
5. Compare the P-value to the significance level: If the P-value is less than or equal to the significance level (α), reject the null hypothesis. In this case, 0.1 > 0.05, so we do not reject the null hypothesis.
Based on the information provided, there is not sufficient evidence at the α=0.05 level to conclude that the proportion of people in Antonia's city that can speak more than one language is greater than 26%.
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A lottery game contains 24 balls numbered 1 through 24. what is the probability of choosing a ball numbered 25? a. 0 c. 24 b. 1 d. startfraction 1 over 24 endfraction
The probability of choosing a ball numbered 25 is 0.
The lottery game contains only 24 balls numbered from 1 to 24. There is no ball numbered 25, so the probability of choosing a ball numbered 25 is 0. The probability of an event is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes.
In this case, the number of favorable outcomes is 0 because there is no ball numbered 25, and the total number of possible outcomes is 24 since there are 24 balls in the game. Therefore, the probability of choosing a ball numbered 25 is 0/24, which simplifies to 0.
Mathematically, the probability of choosing a ball numbered 25 can be calculated as:
P(choosing ball numbered 25) = number of favorable outcomes / total number of possible outcomes
= 0 / 24
= 0
Therefore, the probability of choosing a ball numbered 25 is 0.
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1. If the probability that a light bulb is defective is 0.1, what is the probability that...
a. exactly 3 out of 7 bulbs are defective.
b. exactly 2 out of 5 bulbs are defective.
c. 4 or 5 out of 10 bulbs are defective.
1
d. no bulbs out of 10 are defective.
e. one or more bulbs out of 10 are defective.
Answer:
a. 5.74%.
b. 7.29%
c. 20.18%
d. 34.87%
e. 65.13%
Step-by-step explanation:
a. This problem can be solved using the binomial distribution formula: P(X=k) = (n choose k) * p^k * (1-p)^(n-k), where n is the sample size, k is the number of successes, p is the probability of success, and (n choose k) is the binomial coefficient.
For this problem, n=7, p=0.1, and we want to find P(X=3). Therefore, we have:
P(X=3) = (7 choose 3) * 0.1^3 * (0.9)^4 = 0.0574, or 5.74%.
b. We have n=5, p=0.1, and we want to find P(X=2). Therefore, we have:
P(X=2) = (5 choose 2) * 0.1^2 * (0.9)^3 = 0.0729, or 7.29%.
c. To find the probability that 4 or 5 out of 10 bulbs are defective, we can use the binomial distribution to find the probabilities of each outcome separately and add them together. We have n=10 and p=0.1.
P(4 out of 10 are defective) = (10 choose 4) * 0.1^4 * (0.9)^6 = 0.1937, or 19.37%.
P(5 out of 10 are defective) = (10 choose 5) * 0.1^5 * (0.9)^5 = 0.0081, or 0.81%.
P(4 or 5 out of 10 are defective) = P(4 out of 10 are defective) + P(5 out of 10 are defective) = 0.1937 + 0.0081 = 0.2018, or 20.18%.
d. To find the probability that no bulbs out of 10 are defective, we can use the binomial distribution with n=10 and p=0.1, and find P(X=0). Therefore, we have:
P(X=0) = (10 choose 0) * 0.1^0 * (0.9)^10 = 0.3487, or 34.87%.
e. To find the probability that one or more bulbs out of 10 are defective, we can use the complement rule and subtract the probability of no bulbs being defective from 1. Therefore, we have:
P(one or more bulbs out of 10 are defective) = 1 - P(X=0) = 1 - 0.3487 = 0.6513, or 65.13%.
For the following function, find the Taylor series centered at 4 and give the stronger terms of the Taylor series Wite the intervat of convergence of the series (+) = In(1) (t)= Σ ร f(x) + The welval of convergence is (Give your answer in interval notation)
The Taylor series centered at 4 for f(x) = ln(1+x) is: f(x) = ln(5) + (x-4)/5 - (x-4)^2/50 + (2/125)*(x-4)^3 - (6/625)*(x-4)^4 + ... The interval of convergence for this series is (-∞, ∞).
Let's find the Taylor series centered at 4 for the function f(x) = ln(1+x).
We can use the formula for the Taylor series coefficients:
f^(n)(x) = (-1)^(n-1) * (n-1)! / (1+x)^n
where f^(n)(x) denotes the nth derivative of f(x).
Using this formula, we can find the Taylor series centered at 4: f(4) = ln(1+4) = ln(5) f'(x) = 1/(1+x), so f'(4) = 1/5 f''(x) = -1/(1+x)^2, so f''(4) = -1/25 f'''(x) = 2/(1+x)^3, so f'''(4) = 2/125 f''''(x) = -6/(1+x)^4, so f''''(4) = -6/625 and so on.
Putting it all together, the Taylor series centered at 4 for f(x) is:
f(x) = ln(5) + (x-4)/5 - (x-4)^2/50 + (2/125)*(x-4)^3 - (6/625)*(x-4)^4 + ...
To find the interval of convergence, we can use the ratio test:
lim |(f^(n+1)(x) / f^(n)(x)) * (x-4)/(x-4)| = lim |(-1) * (n+1) * (1+x)^2 / (1+x)^n| * |x-4| = lim (n+1) * (1+x)^2 / (1+x)^n * |x-4| = lim (n+1) / (1+x)^(n-2) * |x-4|
Since this limit is zero for all values of x, the interval of convergence is the entire real line, (-∞, ∞).
So the final answer is: The Taylor series centered at 4 for f(x) = ln(1+x) is: f(x) = ln(5) + (x-4)/5 - (x-4)^2/50 + (2/125)*(x-4)^3 - (6/625)*(x-4)^4 + ... The interval of convergence for this series is (-∞, ∞).
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5. A ramp is to be built using a 20 foot long board and an 18 foot long board. To make die stable, the builders would like to add a third board to create a right triangle. How longed that board be, to the nearest hundredth of a foot?
The length of the third board the builders will add to create a right triangle, according to the Pythagorean Theorem is about 8.72 ft
What is the Pythagorean Theorem?Pythagorean Theorem is the relationship between the lengths of the three sides of a right triangle. The theorem states that the square of the length of the hypotenuse is equivalent to the sum of the square of the other two sides of the right triangle.
The specified dimensions of the ramp are;
Length of one side of the ramp = 20 ft
Length of the other side of the ramp = 18 ft
The shape of the triangle the builders would like to create = A right triangle
Let x represent the length of the third board, and let the 20 ft board represent the hypotenuse side. Pythagorean Theorem indicates that we get;
20² = 18² + x²
20² - 18² = x²
x² = 20² - 18² = 76
x = √(76) = 2·√(19) ≈ 8.72
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CAN SOMEONE SHOW ME STEP BY STEP ON HOW TO DO THIS SOMEONE GAVE ME THE WRONG STEPS
A city just opened a new playground for children in the community. An image of the land that the playground is on is shown.
A polygon with a horizontal top side labeled 45 yards. The left vertical side is 20 yards. There is a dashed vertical line segment drawn from the right vertex of the top to the bottom right vertex. There is a dashed horizontal line from the bottom left vertex to the dashed vertical, leaving the length from that intersection to the bottom right vertex as 10 yards. There is another dashed horizontal line that comes from the vertex on the right that intersects the vertical dashed line, and it is labeled 12 yards.
What is the area of the playground?
900 square yards
855 square yards
1,710 square yards
1,305 square yards
The area of the playground include the following: 900 square yards.
How to calculate the area of a regular polygon?In Mathematics and Geometry, the area of a regular polygon can be calculated by using this formula:
Area = (n × s × a)/2
Where:
n is the number of sides.s is the side length.a is the apothem.In Mathematics and Geometry, the area of a parallelogram can be calculated by using the following formula:
Area of a parallelogram, A = base area × height
Area of playground, A = 45 × 20
Area of a playground, A = 900 square yards.
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Nancy's Cupcakes recorded how many cupcakes it recently sold of each flavor. â
â
âchocolate cupcakes 2
âpistachio cupcakes â 1
âbanana cupcakes â 5
âpumpkin cupcakes â 6
ââConsidering this data, how many of the next 21 cupcakes sold would you expect to be pumpkin cupcakes?â
A
9
B
7
C
6
D
3
Part B
What is probability of a chocolate cupcakes being sold?
â Probability (chocolate cupcakes) =
%
Note: Write your answer as a percentage rounded to the nearest whole number. â
We would expect 9 pumpkin cupcakes to be sold in the next 21 cupcakes. The probability of a chocolate cupcake being sold is approximately 14%.
The question asks to determine how many of the next 21 cupcakes sold would be expected to be pumpkin cupcakes, and also to find the probability of a chocolate cupcake being sold.
First, let's analyze the given data:
- Chocolate cupcakes: 2
- Pistachio cupcakes: 1
- Banana cupcakes: 5
- Pumpkin cupcakes: 6
Total cupcakes sold: 2 + 1 + 5 + 6 = 14
To find the expected number of pumpkin cupcakes in the next 21 sold, calculate the proportion of pumpkin cupcakes in the original data, and then multiply by 21:
(6 pumpkin cupcakes / 14 total cupcakes) * 21 = 9 (rounded)
So, we would expect 9 pumpkin cupcakes to be sold in the next 21 cupcakes (Answer A).
For Part B, we need to find the probability of a chocolate cupcake being sold. To do this, divide the number of chocolate cupcakes by the total number of cupcakes:
Probability (chocolate cupcakes) = (2 chocolate cupcakes / 14 total cupcakes) = 0.142857
Now, convert this probability to a percentage and round to the nearest whole number:
0.142857 * 100 = 14.29% ≈ 14%
So, the probability of a chocolate cupcake being sold is approximately 14%.
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Which of the pair of linear equations has unique solution, no solution or infinitely many solutions. In case there is unique solution find it by using Substitution Method and Elimination Method
(i) x-3y -3=0, 3x-9y-2=0
(ii) 2x+y=5,3x+2y=8
(iii) 3x-5y=20,6x-10y=40
iv) x-3y-7 =0,3x-3y-15=0
v) 8x+5y=9,3x+2y=4
1. x-3y -3=0, 3x-9y-2=0 has no solution
2. 2x+y=5,3x+2y=8 has a unique solution
3. 3x-5y=20,6x-10y=40 has infinitely many solution
4. x-3y-7 =0,3x-3y-15=0 has No solution
5. 8x+5y=9,3x+2y=4 has a unique solution
How to solve the linear equations(i) To solve using substitution method, we can rearrange the first equation to x=3y+3 and substitute it into the second equation:
3(3y+3) - 9y - 2 = 0
9y + 9 - 9y - 2 = 0
7 = 0
This is a contradiction, so the pair of equations has no solution.
(ii) To solve using elimination method, we can multiply the first equation by 2 and subtract it from the second equation:
3x + 2y = 8
(4x + 2y = 10)
-x = -2
So, x = 2. Substituting this value into the first equation, we get:
2x + y = 5
2(2) + y = 5
y = 1
Therefore, the unique solution is (x,y) = (2,1).
(iii) To solve using elimination method, we can multiply the first equation by 2 and subtract it from the second equation:
6x - 10y = 40
(6x - 10y = 40)
0 = 0
This equation is true for any value of x and y, so the pair of equations has infinitely many solutions.
(iv) To solve using elimination method, we can subtract the first equation from the second equation:
3x - 3y - 15 - (x - 3y - 7) = 0
2x - 22 = 0
x = 11
Substituting this value into the first equation, we get:
11 - 3y - 7 = 0
-3y = -4
y = 4/3
Therefore, the unique solution is (x,y) = (11,4/3).
(v) To solve using elimination method, we can multiply the first equation by 2 and subtract it from the second equation:
3x + 2y = 4
(16x + 10y = 18)
-29x - 18y = -14
Solving for y, we get:
y = (29/18)x + (7/9)
Substituting this expression for y into the first equation, we get:
8x + 5((29/18)x + (7/9)) = 9
(143/18)x = 2/9
x = 2/13
Substituting this value into the expression for y, we get:
y = (29/18)(2/13) + (7/9) = 41/117
Therefore, the unique solution is (x,y) = (2/13,41/117).
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Marcos harvests a lot of cherry tomatoes in his garden this year. each day, he keeps one-third and brings the rest into the office to give away. by the time the tomatoes start to get a little mushy, marcos has less than
one eighty first of the original harvest left. how many days after marcos harvested the tomatoes do they start to get a little mushy?
The tomatoes start to get mushy after more than 6 days.
Note: The calculation assumes that the number of tomatoes harvested is large enough for the continuous division process to approach zero.
Let's assume that Marcos initially harvested X cherry tomatoes.
According to the given information, each day Marcos keeps one-third of the tomatoes and brings the remaining amount into the office. This means that after the first day, Marcos would have 2/3 (or 2/3X) of the original harvest left.
On the second day, he would keep one-third of the remaining tomatoes and bring 2/3 × 1/3 (or 2/9) of the original harvest into the office. This would leave him with 2/3 × 2/3 (or 4/9) of the original harvest.
In general, after N days, the amount of tomatoes left can be calculated using the following formula:
Amount of tomatoes left = (2/3)^N × X
The question states that Marcos has less than one eighty-first of the original harvest left when the tomatoes start to get mushy. In other words, when the amount of tomatoes left is less than 1/81 of the original harvest, we can write the following inequality:
[tex](2/3)^N × X < 1/81[/tex]
To find the number of days (N) when the tomatoes start to get mushy, we need to solve for N in the inequality above.
Taking the logarithm (base 2/3) of both sides of the inequality:
[tex]N > log2/3(1/81) / log2/3(2/3)[/tex]
N > 4 / (2/3)
N > 4 × 3/2
N > 12/2
N > 6
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The length of the hypotenuse in a °45 degrees-°45 degrees-°90 degrees triangle is 5 square root of 2. What are the sine and secant ratios for a °45 angle?
The secant of a °45 angle is defined as the ratio of the length of the hypotenuse to the length of the adjacent side. In this case, the adjacent side is also a leg of length 5, so:
secant(45) = hypotenuse/adjacent = 5√2/5 = √2
What is the secant function?The secant function, denoted as sec(x), is a trigonometric function that is defined as the reciprocal of the cosine function, cos(x).
In other words,
sec(x) = 1 / cos(x)
The secant function is defined for all values of x except for those where the cosine function is equal to zero, which corresponds to the values x = (2n+1)π/2 where n is an integer. At these points, the secant function is undefined.
According to the given functionIn a °45-°45-°90 triangle, the two legs are congruent, so if the length of the hypotenuse is 5√2, then each leg has a length of:
leg = hypotenuse/√2 = (5√2)/√2 = 5
The sine of a °45 angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. In this case, the side opposite the angle is a leg of length 5, so:
sine(45) = opposite/hypotenuse = 5/5√2 = 1/√2 = √2/2
The secant of a °45 angle is defined as the ratio of the length of the hypotenuse to the length of the adjacent side. In this case, the adjacent side is also a leg of length 5, so:
secant(45) = hypotenuse/adjacent = 5√2/5 = √2
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